Mathematical Sciences: Studies in Discontinuous Groups and Conformal Geometry

首席研究员将继续他对Klein群、三维几何和拓扑以及不连续群的研究。将对Mobius结构、测地线分层、树上的格子、曲面对称性和某些基本区域进行特别研究。该项目将包括来自群论的数学技术以及一些更标准的几何技术。组是一个抽象的数学对象。整数是群的一个例子，因为人们总是可以在不改变答案的情况下颠倒加法的顺序，存在零，减法总是可能的，加法可以自由地关联。

The principal investigator will continue his studies of Kleinian groups, 3-dimensional geometry and topology, and discontinuous groups. A special investigation will be conducted into Mobius structures, geodesic laminations, lattices on trees, surface symmetries, and certain fundamental domains. The project will encompass mathematical techniques from group theory as well as a number of more standard geometric techniques. A group is an abstract mathematical object. The integers are an example of a group because one can always reverse the order of addition without changing the answer, there is a zero, subtraction is always possible, and additions may be freely associated.